PhD thesis: Shape optimization for thin layers heat exchangers
Published in PhD thesis, University of Chile, University of Pau and Adour Countries, March, 2025
This thesis falls within two major areas of mathematics: numerical analysis of PDEs and shape/ topology optimization. We are interested in the optimal design of a heat exchanger. The aim is to consider the case of a two-fluid heat exchanger in a forced convection regime, in the case where the fluids are separated by a thin solid layer. Then, by addressing challenges arising from non-standard transmission conditions, this work contributes to advancing the theoretical and computational tools used to tackle coupled physical systems in shape optimization.
We begin by proposing an asymptotic model that takes into account heat exchange in the thin solid layer involving Ventcel-type transmission conditions at the interface. Firstly, the numerical resolution of this model is studied and we develop and analyze a Nitsche-type finite element method providing consistency, stability, and error estimates, validated both theoretically and numerically. Secondly, we turn to a shape optimization problem motivated by thermal insulation: we compute shape derivatives for the optimal design problem of minimizing the heat flux outside a pipe surrounded by a thermal insulation of fixed volume, and we implement numerical simulations using the level set method. Finally, we focus on the design of 3D fluid-to-fluid heat exchangers: to maximize heat exchange under energy dissipation and volume constraints, we consider a coupled model involving steady-state Navier-Stokes equations and a convection-diffusion equation with Ventcel-type transmission conditions, analyze the shape sensitivity of the system, and provide 3D numerical simulations.
\textbf{Keywords:} Shape optimization; level-set method; asymptotic model; Ventcel transmission conditions; Nitsche extended finite elements; Navier-Stokes equations; convection-diffusion equation.
Recommended citation: R. Zelada. Shape optimization for thin layers heat exchangers. PhD thesis, University of Chile, University of Pau and Adour Countries, March 2025. Available at https://repositorio.uchile.cl/handle/2250/205114.
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